To illustrate the effectivity of Schwarz preconditioning incorporated in a multigrid cycle in providing a robust solution procedure that is not affected by either the cut elements or by the size of the system, we consider the \(\mu \) CT-scanned trabecular bone specimen displayed in Figure REF . This geometry was first studied in [1]} and the presented results were previously published in [2]}. The specimen is compressed with an average uniaxial strain of \(1\%\)  in the horizontal direction, resulting in the (Frobenius norm) stresses indicated by the colors. Three different meshes are considered, consisting of \(32^3\) , \(64^3\)  and \(128^3\)  elements in the ambient domain. Figure REF  shows the active elements of the coarsest mesh on the right half of the geometry. With quadratic basis functions, these different meshes result in, respectively, \(182\cdot 10^3\) , \(1.03\cdot 10^6\)  and \(6.65\cdot 10^6\)  active degrees of freedom. Figure REF  shows the convergence behavior of the conjugate gradient solver preconditioned by a multigrid cycle with a tailored multiplicative Schwarz smoother for the different discretizations. It can be observed that the convergence is virtually independent of both the cut elements and the size of the system. For details regarding this example the reader is referred to [2]}.
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